A parachuter falls from an altitude of 4500 yards to 1500 yards over 3 minutes. What
is his average distance fallen over the three minutes?
1500 yards per
minute
-1000 yards per
minute
-1500 yards per
minute
1000 yards per
minute

The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

the bottom one

Step-by-step explanation:

its distributive property. 5x11+5x7

Answer:

Negative means focused on what is bad or lacking. A negative ad tells you bad things about the competition. A negative person loves to complain. In math, a negative number is less than zero.

Step-by-step explanation:

Answer:

Square

Rectangle

Step-by-step explanation:

not a pro at shapes.

Answer:

7

Step-by-step explanation:

reminder that the absolute value function always gives a positive result.

3 | - d + 2 | + 1 ( substitute d = 4 )

3 | - 4 + 2 | + 1

= 3 | - 2 | + 1

= 3 × 2 + 1

= 6 + 1

= 7

no entiendo cómo es eso mándame la foto mejor

The values of RS and ST for the collinear points R, S and T are RS = 66 and ST = 49.

When points are collinear, it means they lie on the same straight line. In this case, we are given three collinear points R, S, and T, and the lengths of RS, ST, and RT.

Let's use the fact that the sum of the lengths of RS and ST equals the length of RT.

This gives us the equation:

RS + ST = RT

Substituting the given values, we get:

(8y + 2) + (5y + 9) = 115

Simplifying this equation, we get:

13y + 11 = 115

Solving for y, we get:

y = 8

Now that we know the value of y, we can find the values of RS and ST:

RS = 8y + 2 = 66

ST = 5y + 9 = 49

Therefore, RS = 66 and ST = 49.

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Complete question

Use the number line below, where RS=8y+2, ST=5y+9, and RT=115

Find the value of RS and ST,

The equation of the circle centered at the origin and passing through the point (0, 9)The equation of a circle with the center (h, k) and the radius r is given by the equation as:

(x - h)² + (y - k)² = r².

Therefore, if the center of the circle is at the origin (0, 0), then the equation of the circle is: x² + y² = r², where r is the radius of the circle.Given that the circle passes through the point (0, 9), we can substitute the coordinates of the point into the equation of the circle and solve for r.

Therefore, we have: 0² + 9² = r²81 = r²r = 9

So, the equation of the circle centered at the origin and passing through the point (0, 9) is:x² + y² = 9²

which simplifies to:x² + y² = 81.

This is the required equation of the circle.

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When a plane intersects both nappes of a double-napped cone but does not go through the vertex of the cone, it forms a hyperbola.

A double-napped cone is a three-dimensional object with two identical nappes, or curved surfaces, that meet at a single vertex. The nappes extend infinitely in both directions away from the vertex.

When a plane intersects the double-napped cone, it cuts through both nappes, resulting in a curve that consists of two separate branches. These branches are symmetrical about the plane that contains the axis of the cone.

The resulting curve, known as a hyperbola, has two distinct arms or branches that open up in opposite directions. The hyperbola is characterized by its center, vertices, asymptotes, and foci. The plane intersects the cone at an angle, which determines the shape and orientation of the hyperbola.

Therefore, when a plane intersects both nappes of a double-napped cone but does not go through the vertex, it forms a hyperbola.

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Answer:

his dad was cutting the grass for 1 hour and 4 minutes i hope this helps

Step-by-step explanation:

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

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The ideal way to organize electronically the raw data for a study is to use a spreadsheet or database management system.

A spreadsheet or database management system allows you to input, store, and manage large amounts of data in a structured and organized manner. This makes it easier to analyze and process the data, as well as share it with others working on the study. Using these tools, you can sort, filter, and manipulate the data to find patterns, trends, and insights, making it easier to draw conclusions from the raw data.

Utilizing a spreadsheet or database management system is the most effective and efficient way to organize raw data electronically for a study, as it provides structure, organization, and ease of data manipulation.

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Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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The age of the skull is 7000 years as  half-life of C-14 is 5,700 years.

The half-life of C-14 is 5,700 years.

This means that after 5,700 years, the amount of C-14 in a sample is reduced to half of its original amount.

Let A₀ be the original amount of C-14 in the skull. Then, after some time t, the amount of C-14 remaining is 43% of A₀.

This can be expressed as:

\(0.43A_0 = A_0e^(^-^k^t^)\)

Simplifying this equation, we get

\(e^(^-^k^t^) = 0.43\)

Taking the natural logarithm of both sides, we get:

-ln(0.43) = -kt

Solving for t, we get:

t = (ln(0.43))/k

The value of the decay constant k for C-14 is approximately 0.00012 per year.

Substituting the values, we get:

t = (ln(0.43))/0.00012

=7000 years

Therefore, the age of the skull is approximately 7000 years.

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The indefinite integral of (1 / 1+e^12x) is (1/12) ln|1+e^12x| + C, where C is the constant of integration.

To find the indefinite integral of (1 / 1+e^12x), we can use a table of integrals with forms involving eu. The form that matches our integral is ∫(1 / 1+e^u) du, where u=12x.

We can substitute u=12x and du/dx=12 to get ∫(1 / 1+e^12x) dx = (1/12) ∫(1 / 1+e^u) du.

Using the table of integrals, the integral of (1 / 1+e^u) du is ln|1+e^u| + C, where C is the constant of integration.

Substituting back in u=12x and multiplying by 1/12, we get the final answer: ∫(1 / 1+e^12x) dx = (1/12) ln|1+e^12x| + C.

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Answer:

it is right answer .you can write as type solution

The number of triangles with all three vertices in the interior of the circle that are created Since we have chosen 8 points on a circle and every pair of points is connected with a chord, the total number of chords will be 28 (by choosing any two points from 8 points.

We get the number of chords which is given by the formula $\frac{n(n-1)}{2}$). Also, no three chords intersect in a single point inside the circle. Therefore, every triangle will be formed by selecting 3 chords from the total 28 chords. But, we need to remember that some of these triangles will lie on the circle.

We know that if we choose three points on a circle, then a triangle will lie on the circle. Thus, to find the number of triangles that lie on the circle, we need to choose any three points from 8 points on the circle. Thus, the number of triangles with all three vertices in the interior of the circle that are created is:$$\ large 3520-56=3464$$ Hence, the main answer is 3464.

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Graph-X represents the given set of inequalities.

"An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions."

Given two inequalities are:

1. y > (1/3)x - 2

If we compare it with the slope-intercept form of a line, then:

Slope = 1/3, y-intercept = - 2

Therefore, the line cuts the y-axis at x = - 2.

Here, the greater than sign indicates that the graph would be shaded down.

2. y < - 4x - 2

If we compare it with the slope-intercept form of a line, then:

Slope = - 4, y-intercept = - 2

Therefore, the line cuts the y-axis at x = - 2.

Here, the less than sign indicates that the graph would be shaded up.

Therefore, Graph-X represents the given set of inequalities.

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The scale for the model length of the fuselage obtained by taking the ratio of the model length and the actual length is 0.125

Actual Length of fuselage = 170 feets

Length of fuselage on model = 21.25

To obtain the scale of the model, we take the ratio of the model length and the actual length :

Therefore, the scale for the model length of the fuselage is 0.125

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A) 500

B) 54 minutes

C) 68cents and 60 cents

D)

E) $40.95

A proportion is a statement that says that two ratios are equal. They can be used in many everyday situations like comparing sizes, cooking, calculating percentages, and more.

Proportions can be written as equivalent fractions or as equal ratios.

A) 42% = 210

100% = (210 x 100)/42

= 500 people

B) 135 berries = 15 minutes

    486 berries = ??minutes

= (486 x 15)/135

= 54 minutes

C) unit price = $6.75/10 = 0.675cents or 68cents

    ii) unit price = $7.25/12 = 0.604cents or 60cents

D) Inconclusive question.

E) 40% of 65 = $26

65 - 26 = $39

Tax = 5% = $1.95

Total = $39 + 1.95

Final Price of jacket = $40.95

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Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

Step-by-step explanation:

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The conclusion that red is the preferred color of shirt among 7th grade students based on a survey of 6 random students in an art class is not necessarily valid due to the small sample size, sampling bias, and lack of generalizability.

The sample size of six pupils is tiny and may not be typical of the overall seventh-grade population. It's probable that the six students in the art class have different preferences or biases than the other seventh-grade students.

Also, the sample of six pupils is drawn at random from an art class rather than from the total 7th grade population. Students who are interested in art may have different preferences than students who are not. This can add bias into the sample.

Finally, the language of the survey question is critical. If the survey question specifically asks about the most chosen color of shirt among 7th grade kids in general, the conclusion that red is the most preferred color of shirt follows.

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The probability that a daily average over a given month is greater than x is 2.5% , the value of x is 232.08

Given:

Mean of number of diners is 138

Standard deviation of diners is 48

(Mean and standard deviation does not follow a normal distribution necessarily.)

Let z be the standardized variable that is z= (X- μ)/ σ

where, mean = μ and standard deviation =σ

Such as Z follows N(μ,σ) = N(0,1)

We know that in continuous distribution, probability of a single point is 0, so we can write

P( Z<=z)= P(Z<z)

For the given case, let the random variable X tracks the number of dinners at given restaurant. Assuming normal distribution being pertained by X, we get:

X follows N(138,48)

The given data shows that:

2.5% of all daily averages records lie bigger than value X = x

or

P(X > x) = 2.5%  0.025

Converting it to standard normal distribution(so that we can use z tables and p values to get the unknown x), we get:

z= (x-138)/48

The given probability statement is expressed as:

P(Z>z)=0.025

P( Z<=z)=0.975

We get z = 1.96.

Thus

z=1.96= (x- 138)/48

=> x=232.08

Thus, the value of x is 232.08 approximately.

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The correct option is B. revised probability

Bayes' Theorem:

Bayes' Theorem, named after 18th-century British mathematician Thomas Bayes, is a mathematical formula for determining conditional probability. Conditional probability is the likelihood of an outcome occurring, based on a previous outcome having occurred in similar circumstances. Bayes' theorem provides a way to revise existing predictions or theories (update probabilities) given new or additional evidence.

In finance, Bayes' Theorem can be used to rate the risk of lending money to potential borrowers. The theorem is also called Bayes' Rule or Bayes' Law and is the foundation of the field of Bayesian statistics.

KEY TAKEAWAYS

The correct option is B. revised probability

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The angle that a 20-foot ramp must make with the ground to reach the same window is 90°.

In order to reach a certain window, a 10-foot ramp must make an angle of 30° with the ground.

The angle that a 20-foot ramp must make with the ground to reach the same window is equal to the angle whose opposite side is twice the hypotenuse of the 10-foot ramp and whose hypotenuse is twice the hypotenuse of the 10-foot ramp.

Using the sine rule, sin θ = (opp/hyp).For the 10-foot ramp, sin 30° = (10/hyp).hyp = 10/sin 30°hyp = 20 ft.

For the 20-foot ramp, sin θ = (2 × 20)/40 = 1.sin θ = sin 90°θ = 90°.

Therefore, the angle that a 20-foot ramp must make with the ground to reach the same window is 90°.

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